Alcohol is mainly comprised of ethanol, plus a very small amount of methanol. When you consume an alcoholic drink, your body breaks down the ethanol first, and relatively harmless by-products are produced. Next the methanol breaks down and produces a toxin, which causes hangover symptoms.
Putting more alcohol back into your system (‘hair of the dog’) relieves some of the hangover symptoms because you start breaking down ethanol again. You feel better until the methanol starts to metabolise and the hangover symptoms return.
This ‘treatment’ is very unwise, unless you are planning on being permanently drunk. When it comes to hangovers, prevention is much better than cure!